Precalculus Week 1 Video Clip 01 copy cal01

• How could we determine whether the depth of the water is changing at a constant, decreasing or increasing rate?
• How could we determine whether the range of the water stream is increasing a constant, decreasing or increasing rate?
• How is the range of the stream related to the rate of which the water level changes?
• Is the rate at which the water level changes related to the rate of which the range of the stream changes?

Precalculus Week 1 Video Clip 02 copy cal02

• Is the graph of depth vs. time increasing or decreasing?
• Is the depth changing and increasing, a decreasing or a consta nt rate, and how would each of these possibilities be seen in the shape of the graph?

Precalculus Week 1 Video Clip 03 describes depth vs. clock time data, asks about evidence for way rate changes, for graph shape from the table

• How does the depth vs. clock time data give us evidence for the shape of the graph?

Precalculus Week 1 Video Clip 04 evidence for slowing of flow, idea of rate

• What evidence is there in the table of data for the speeding up or slowing down of the flow?

Precalculus Week 1 Video Clip 05 the graph of the data, steepness indicates rate

• How is the steepness of the graph related to the rate at which water flows from the cylinder? What does the steepness of the graph tell us about the way water flows from the cylinder?

Precalculus Week 1 Video Clip 06 columns for `dt, `dy, `dy/`dt; rate calculations

• Given the table of y = depth vs. t = clock time data, how do we calculate the corresponding time and depth intervals `dt and `dy, and how we represent these quantities on the table?
• How do we calculate the average rates `dy / `dt? Why we call these average rates? What do they tell us about the water in the cylinder?

Precalculus Week 1 Video Clip 07 rate calculations and slope

• How are our rate calculations represented graphically by the slope?

Precalculus Week 1 Video Clip 08 is there a mathematical rule, a function, that predicts these quantities? If so, call it a mathematical model.

• Why would we expect that there exists a mathematical rule or function that predicts the depth y vs. time t for the flow situation?

Precalculus Week 1 Video Clip 09 y = x^2 to general quadratic: stretching, shifting, always gives quadratic, every quadratic can be so obtained

• Why does it seem reasonable that by stretching in shifting the y = t^2 graph we should obtain a graph that models be observed depth vs. time data?

Precalculus Week 1 Video Clip 10 choosing points and obtaining simul. eq. with 3 parameters.

• How by choosing three points do we obtain three simultaneous equations for the three parameters of the quadratic model?
• What are the three parameters of the quadratic model?
• What are some of the things we should think about as we choose the points to put into our quadratic model?

Precalculus Week 1 Video Clip 11 eliminating c

• How do we eliminate a variable from a system of three simultaneous equations in three unknowns to obtain a system of two simultaneous equations in two unknowns?

Precalculus Week 1 Video Clip 12 eliminating b, obtaining a

• Given a system of two simultaneous equations into unknowns, how do we eliminate one of the unknown and solve for the value of the other?

Precalculus Week 1 Video Clip 13 back substitution, plugging into form to get model

• Once we have found the value of one of the variables, how do we use back substitution to find the values of the others?

Precalculus Week 1 Video Clip 14 comparing model with data: deviations and residuals

• How do we find the deviations and residuals of our model, and what do they tell us about the quality of our model?
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Introduction to CD #2:   Brief Overview of Major Topics, Class Notes 1-6

Class Notes #01:  Depth vs. Clock Time Model

Class Notes #02: Quadratic Model of Depth vs. Clock Time (3 points, 3 simultaneous equations)

Class Notes #03: Graphs of Quadratic Functions

Class Notes #04: Graphs of Quadratics Functions; Function Notation

Class Notes #05: Introduction to Function Families

#08: Symbolic Slopes; Slope = Slope Equation

#09: Linear Functions

#10: Proportionality and Sand Piles

#11: Proportionality

#12: Proportionality, Laws of Exponents, Sequences

#15: Test Questions; Behavior of Exponential Functions

#16: Exponential Functions: Inverse Functions and Logarithms

#17: Using Logarithms

#18: Logarithms: Modeling Exponential Behavior